Related papers: Spectral Topology and Delocalization in Disordered…
We calculated numerically the localization length of one-dimensional Anderson model with diagonal disorder. For weak disorder, we showed that the localization length changes continuously as the energy changes from the band center to the…
We study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly…
A new type of delocalization induced by coherent harmonic perturbations in one-dimensional Anderson-localized disordered systems is investigated. With only a few $M$ frequencies a normal diffusion is realized, but the transition to…
We study two-particle states in a Su-Shrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with…
It is shown that, an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight binding model can be tailored to generate absolutely continuous energy bands. It can be…
We investigate the directional localization properties of wave-functions in a two-dimensional tight-binding model with uniform hopping and correlated random on-site energies. By controlling the disorder correlation strength with a parameter…
We introduce a network model to describe two-dimensional disordered electron systems with spin-orbit scattering. The network model is defined by a discrete unitary time evolution operator. We establish by numerical transfer matrix…
Topological insulator lie at the forefront of condensed matter physics. However strong disorder can destroy the topological states and make all states become localized. In this paper, we investigate the competition between topology and…
We investigate finite two-dimensional disordered systems with periodic confinement. At low energies, eigenstates exhibit strong Anderson localization, while at higher energies a subset of states exhibits variational scarring with…
We analyse the anomalous properties of specific electronic states in the Kronig-Penney model with weak compositional and structural disorder. Using the Hamiltonian map approach, we show that the localisation length of the electronic states…
We present strong numerical evidence for the existence of a localization-delocalization transition in the eigenstates of the 1-D Anderson model with long-range hierarchical hopping. Hierarchical models are important because of the…
Non-Hermitian systems can exhibit unique topological and localization properties. Here we elucidate the non-Hermitian effects on disordered topological systems by studying a non-Hermitian disordered Su-Schrieffer-Heeger model with…
Localization in non-Hermitian quasicrystals can differ fundamentally from its Hermitian counterpart when non-reciprocity is spatially disordered. Here we study a one-dimensional non-Hermitian Aubry-Andr\'{e}-Harper chain with a Bernoulli…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
Anderson localization, the absence of diffusive transport in disordered systems, has been manifested as hopping transport in numerous electronic systems, whereas in recently discovered topological insulators it has not been directly…
We consider critical eigenstates in a two dimensional quasicrystal and their evolution as a function of disorder. By exact diagonalization of finite size systems we show that the evolution of properties of a typical wave-function is…
Influence of disorder on the temperature of superconducting transition (T_c) is studied within the sigma-model renormalization group framework. Electron-electron interaction in particle-hole and Cooper channels is taken into account and…
In this work we study the spectral properties of the adjacency matrix of critical Erd\"os-R\'enyi (ER) graphs, i.e. when the average degree is of order \log N. In a series of recent inspiring papers Alt, Ducatez, and Knowles have rigorously…
We investigate the statistics of eigenstates in a weak self-affine disordered potential in one dimension, whose Gaussian fluctuations grow with distance with a positive Hurst exponent $H$. Typical eigenstates are superlocalized on samples…
Scale-free localization in non-Hermitian systems is a distinctive type of localization where the localization length of certain eigenstates, known as scale-free localized (SFL) states, scales proportionally with the system size. Unlike skin…